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Considering a degree in Chemical?
These rankings show the most affordable colleges for Chemical majors who live in Pennsylvania.
Rankings are calculated by estimating the net price at every college offering Chemical degrees for a "typical" middle class family living in the state of Pennsylvania.
Note: Net price is the actual cost of college paid after factoring in financial aid.The net prices displayed in these rankings are College Raptor's estimates.
“Typical” middle class family values used in the Net Price estimates on this page are:
| Rank | Institution | Typical Net Price | Sticker Price | % Savings | Undergraduates | Est. Median SAT | Acceptance Rate | Save |
|---|---|---|---|---|---|---|---|---|
| 1 | United States Coast Guard Academy | 0 | 0 | 0 | 1,108 | 1334 | 0.2244 | |
| 1 | United States Military Academy | 0 | 0 | 0 | 4,473 | 1326 | 0.1245 | |
| 1 | United States Naval Academy | 0 | 0 | 0 | 4,474 | 1305 | 0.0927 | |
| 4 | Johns Hopkins University | 2700 | 92000 | 0.9704 | 6,356 | 1543 | 0.0644 | |
| 5 | Princeton University | 4000 | 82600 | 0.9516 | 5,813 | 1535 | 0.0462 | |
| 6 | Yale University | 5500 | 92200 | 0.94 | 6,814 | 1507 | 0.0387 | |
| 7 | Harvard University | 5900 | 95400 | 0.9378 | 8,844 | 1535 | 0.0365 | |
| 8 | Carnegie Mellon University | 6800 | 90200 | 0.9249 | 7,377 | 1528 | 0.1166 | |
| 9 | California Institute of Technology | 7500 | 91800 | 0.9183 | 987 | 1557 | 0.0257 | |
| 10 | Vanderbilt University | 7800 | 96200 | 0.9185 | 7,221 | 1527 | 0.0586 | |
| 11 | Brigham Young University | 8000 | 22000 | 0.6362 | 32,952 | 1374 | 0.6778 | |
| 11 | Massachusetts Institute of Technology | 8000 | 90000 | 0.9116 | 4,535 | 1542 | 0.0455 | |
| 13 | Bowdoin College | 8100 | 89900 | 0.9101 | 1,881 | 1505 | 0.0713 | |
| 14 | Columbia University in the City of New York | 8400 | 97100 | 0.914 | 9,164 | 1535 | 0.0399 | |
| 15 | Swarthmore College | 8500 | 92800 | 0.9081 | 1,623 | 1520 | 0.0746 | |
| 16 | Washington University in St Louis | 9300 | 102300 | 0.9091 | 8,220 | 1513 | 0.1206 | |
| 17 | Rice University | 9800 | 89100 | 0.8903 | 4,789 | 1535 | 0.08 | |
| 17 | Wellesley College | 9800 | 91300 | 0.8928 | 2,407 | 1500 | 0.1405 | |
| 19 | University of Notre Dame | 10900 | 86200 | 0.874 | 8,880 | 1500 | 0.1127 | |
| 20 | University of Pennsylvania | 11100 | 92700 | 0.8803 | 11,478 | 1536 | 0.054 | |
| 21 | University of Tulsa | 11400 | 62900 | 0.8184 | 2,852 | 1328 | 0.6151 | |
| 22 | University of Washington-Seattle Campus | 11600 | 29100 | 0.6019 | 40,684 | 1331 | 0.3915 | |
| 23 | Cornell University | 11700 | 93100 | 0.8745 | 16,128 | 1521 | 0.0876 | |
| 24 | University of Chicago | 12200 | 95500 | 0.872 | 7,598 | 1535 | 0.0448 | |
| 25 | California State Polytechnic University-Pomona | 12600 | 12600 | 0 | 25,255 | 1134 | 0.7517 | |
| 25 | Lamar University | 12600 | 22900 | 0.4492 | 8,184 | 1050 | 0.8641 | |
| 27 | New Mexico State University-Main Campus | 12800 | 26500 | 0.5164 | 12,507 | 1010 | 0.8897 | |
| 28 | Lafayette College | 12900 | 84800 | 0.848 | 2,775 | 1427 | 0.3145 | |
| 28 | North Carolina A & T State University | 12900 | 17900 | 0.2801 | 12,497 | 1075 | 0.499 | |
| 30 | University of Wisconsin-Stevens Point | 13000 | 24700 | 0.474 | 7,490 | 1140 | 0.918 | |
| 31 | University of South Florida | 13100 | 17100 | 0.2337 | 38,525 | 1239 | 0.4319 | |
| 32 | University of Delaware | 13600 | 34500 | 0.606 | 20,026 | 1294 | 0.706 | |
| 33 | University of Wisconsin-Madison | 13700 | 50700 | 0.7294 | 38,040 | 1418 | 0.452 | |
| 34 | University of Houston | 13900 | 22000 | 0.3675 | 39,257 | 1249 | 0.7392 | |
| 35 | University of Idaho | 14200 | 25800 | 0.4504 | 9,574 | 1119 | 0.7553 | |
| 36 | Central Michigan University | 14500 | 37800 | 0.6157 | 10,193 | 1095 | 0.8982 | |
| 37 | Stanford University | 14800 | 71700 | 0.794 | 7,904 | 1535 | 0.0361 | |
| 38 | University of St Thomas | 15100 | 50900 | 0.7036 | 3,365 | 1095 | 0.8992 | |
| 39 | Case Western Reserve University | 15200 | 91300 | 0.8339 | 6,528 | 1475 | 0.3654 | |
| 39 | University of California-Irvine | 15200 | 38000 | 0.6003 | 30,204 | 1333 | 0.2857 | |
| 41 | The University of Texas at Tyler | 15300 | 24900 | 0.385 | 7,683 | 1120 | 0.9402 | |
| 42 | Western Michigan University | 15400 | 26500 | 0.4193 | 13,027 | 1115 | 0.846 | |
| 43 | Florida State University | 15600 | 22900 | 0.3184 | 32,720 | 1360 | 0.2422 | |
| 44 | Northeastern University | 15700 | 89900 | 0.8254 | 17,432 | 1490 | 0.0522 | |
| 45 | Lehigh University | 15900 | 88600 | 0.8206 | 5,911 | 1436 | 0.2593 | |
| 45 | University of Illinois Urbana-Champaign | 15900 | 38400 | 0.5856 | 37,140 | 1406 | 0.4237 | |
| 47 | University of California-Riverside | 16000 | 36500 | 0.5612 | 22,600 | 1199 | 0.7639 | |
| 48 | Commonwealth University of Pennsylvania | 16100 | 26900 | 0.4031 | 9,847 | 1090 | 0.9309 | |
| 48 | University of Kansas | 16100 | 34900 | 0.5377 | 22,085 | 1176 | 0.9348 | |
| 50 | University of California-Los Angeles | 16300 | 36700 | 0.5554 | 33,475 | 1399 | 0.0897 | |
| 51 | University of Florida | 16400 | 22500 | 0.271 | 36,573 | 1399 | 0.242 | |
| 52 | Wayne State University | 16500 | 32900 | 0.4982 | 16,012 | 1174 | 0.8116 | |
| 53 | West Virginia University | 16600 | 40900 | 0.5939 | 18,206 | 1125 | 0.89 | |
| 54 | Northwestern University | 16700 | 89500 | 0.8138 | 9,399 | 1527 | 0.0769 | |
| 54 | University of Maine | 16700 | 29300 | 0.4303 | 9,601 | 1205 | 0.9664 | |
| 56 | University of Massachusetts-Lowell | 16800 | 35700 | 0.5295 | 12,122 | 1283 | 0.8304 | |
| 57 | West Chester University of Pennsylvania | 17100 | 17100 | 0.0005 | 14,449 | 1195 | 0.784 | |
| 58 | Centre College | 17500 | 73000 | 0.7603 | 1,404 | 1314 | 0.5436 | |
| 58 | Texas A&M University-College Station | 17500 | 29900 | 0.4159 | 60,710 | 1278 | 0.5743 | |
| 60 | University of Louisville | 17600 | 29100 | 0.3956 | 17,086 | 1148 | 0.7941 | |
| 61 | University of Miami | 17700 | 95700 | 0.8149 | 13,250 | 1406 | 0.189 | |
| 62 | Georgia Institute of Technology-Main Campus | 17900 | 44300 | 0.5956 | 20,591 | 1435 | 0.1407 | |
| 63 | California State University Maritime Academy | 18100 | 48400 | 0.6263 | 804 | 1110 | 0.9501 | |
| 64 | The University of Texas Permian Basin | 18200 | 28600 | 0.3634 | 4,218 | 1030 | 0.9489 | |
| 64 | University of Pittsburgh-Johnstown | 18200 | 35400 | 0.4852 | 1,813 | 1109 | 0.9484 | |
| 66 | Texas Tech University | 18400 | 27100 | 0.3216 | 32,580 | 1200 | 0.7265 | |
| 67 | McNeese State University | 18900 | 27400 | 0.3102 | 5,668 | 1060 | 0.7827 | |
| 68 | University of Illinois Chicago | 19000 | 30100 | 0.3693 | 22,495 | 1252 | 0.7735 | |
| 69 | University of Nevada-Reno | 19300 | 28200 | 0.3154 | 19,117 | 1134 | 0.7371 | |
| 70 | University of Missouri-Columbia | 19400 | 36900 | 0.4748 | 24,449 | 1256 | 0.7847 | |
| 70 | University of South Alabama | 19400 | 22400 | 0.1342 | 9,241 | 1140 | 0.7096 | |
| 72 | University of Mississippi | 19500 | 27000 | 0.2777 | 21,585 | 1182 | 0.9658 | |
| 73 | Pennsylvania Western University | 19600 | 29100 | 0.3269 | 7,586 | 1045 | 0.9433 | |
| 74 | University of Alabama in Huntsville | 19900 | 30500 | 0.3473 | 6,800 | 1293 | 0.6857 | |
| 74 | University of Virginia-Main Campus | 19900 | 78600 | 0.7467 | 17,885 | 1470 | 0.1681 | |
| 76 | Iowa State University | 20000 | 24200 | 0.1732 | 25,628 | 1207 | 0.8866 | |
| 76 | Youngstown State University | 20000 | 34000 | 0.4118 | 9,400 | 1115 | 0.8445 | |
| 78 | University of Southern California | 20100 | 75900 | 0.7356 | 20,630 | 1492 | 0.0981 | |
| 79 | University of Rochester | 20200 | 93100 | 0.7833 | 6,580 | 1462 | 0.4008 | |
| 79 | Villanova University | 20200 | 87900 | 0.7702 | 7,004 | 1457 | 0.2698 | |
| 81 | Ohio University-Main Campus | 20500 | 23200 | 0.1164 | 20,444 | 1209 | 0.8499 | |
| 82 | University of Wyoming | 20700 | 27900 | 0.2594 | 8,130 | 1179 | 0.9688 | |
| 83 | Washington State University | 21200 | 36200 | 0.4131 | 21,455 | 1125 | 0.8664 | |
| 84 | Louisiana Tech University | 21500 | 26100 | 0.1764 | 10,881 | 1189 | 0.864 | |
| 85 | Bucknell University | 21700 | 88600 | 0.7547 | 3,920 | 1396 | 0.2893 | |
| 85 | Tufts University | 21700 | 98900 | 0.7803 | 7,126 | 1507 | 0.1149 | |
| 87 | Colorado State University-Fort Collins | 21800 | 37300 | 0.4156 | 26,221 | 1204 | 0.8854 | |
| 88 | Montana State University | 22300 | 27100 | 0.1769 | 15,046 | 1184 | 0.8214 | |
| 88 | Virginia Commonwealth University | 22300 | 33600 | 0.336 | 21,210 | 1148 | 0.9262 | |
| 90 | New York University | 22600 | 91800 | 0.7535 | 29,060 | 1520 | 0.0923 | |
| 91 | University of New Mexico-Main Campus | 23000 | 27500 | 0.1618 | 17,450 | 1044 | 0.9518 | |
| 92 | San Jose State University | 23100 | 41100 | 0.4381 | 28,008 | 1124 | 0.8461 | |
| 93 | Kutztown University of Pennsylvania | 23600 | 32100 | 0.2651 | 6,306 | 1214 | 0.9075 | |
| 94 | University of South Carolina-Columbia | 23700 | 24900 | 0.0481 | 30,187 | 1292 | 0.6015 | |
| 95 | University of Kentucky | 23800 | 36400 | 0.3453 | 25,534 | 1193 | 0.9294 | |
| 96 | University of Massachusetts-Amherst | 24100 | 39300 | 0.3873 | 23,920 | 1397 | 0.5973 | |
| 97 | Miami University-Oxford | 24400 | 27500 | 0.1129 | 16,816 | 1299 | 0.754 | |
| 97 | University of North Carolina Wilmington | 24400 | 24400 | 0 | 15,254 | 1270 | 0.6424 | |
| 99 | New Jersey Institute of Technology | 24600 | 30600 | 0.1961 | 10,200 | 1325 | 0.6507 | |
| 100 | University of Pittsburgh-Pittsburgh Campus | 24900 | 40600 | 0.3868 | 25,900 | 1375 | 0.5808 | |
| 101 | Tennessee Technological University | 25000 | 33700 | 0.257 | 9,187 | 1163 | 0.7613 | |
| 102 | California State Polytechnic University-Humboldt | 25300 | 37900 | 0.3322 | 5,661 | 1085 | 0.982 | |
| 103 | Clarkson University | 25600 | 78000 | 0.672 | 2,296 | 1302 | 0.7736 | |
| 104 | Christian Brothers University | 25900 | 57600 | 0.5497 | 1,155 | 1110 | 0.867 | |
| 105 | Stony Brook University | 26100 | 33200 | 0.2129 | 18,263 | 1410 | 0.4904 | |
| 106 | Dordt University | 26200 | 52500 | 0.5007 | 1,716 | 1205 | 0.6847 | |
| 107 | South Dakota School of Mines and Technology | 26300 | 28400 | 0.0757 | 2,216 | 1268 | 0.7987 | |
| 107 | Tuskegee University | 26300 | 42100 | 0.3757 | 2,659 | 1090 | 0.4868 | |
| 109 | University of Southern Mississippi | 26500 | 26500 | 0 | 10,193 | 1181 | 0.9912 | |
| 110 | Trine University | 26600 | 56100 | 0.5253 | 4,373 | 1159 | 0.8548 | |
| 111 | University of Arkansas | 26700 | 28900 | 0.0745 | 28,859 | 1179 | 0.743 | |
| 112 | Kansas State University | 27100 | 30400 | 0.1087 | 15,650 | 1164 | 0.8169 | |
| 112 | University of Arizona | 27100 | 38100 | 0.2888 | 44,848 | 1233 | 0.8614 | |
| 114 | Rowan University | 27500 | 41300 | 0.3345 | 16,100 | 1219 | 0.7766 | |
| 115 | University of Maryland-Baltimore County | 27600 | 27600 | 0 | 10,767 | 1326 | 0.7243 | |
| 116 | University of Nebraska-Lincoln | 27900 | 32800 | 0.148 | 19,701 | 1214 | 0.8749 | |
| 117 | Pennsylvania State University-Main Campus | 28000 | 41600 | 0.3261 | 42,604 | 1336 | 0.6056 | |
| 118 | Mississippi State University | 28200 | 32300 | 0.1283 | 18,567 | 1214 | 0.7764 | |
| 118 | Syracuse University | 28200 | 83100 | 0.6604 | 15,957 | 1363 | 0.4592 | |
| 120 | Lincoln Memorial University | 28600 | 44900 | 0.3627 | 1,668 | 1085 | 0.6259 | |
| 120 | University of Akron Main Campus | 28600 | 32300 | 0.1145 | 11,160 | 1069 | 0.5967 | |
| 122 | University of Dayton | 28900 | 64200 | 0.5499 | 7,740 | 1302 | 0.6545 | |
| 122 | University of Utah | 28900 | 32000 | 0.0984 | 28,064 | 1237 | 0.8598 | |
| 124 | University of Iowa | 29000 | 31100 | 0.0691 | 22,738 | 1208 | 0.8362 | |
| 125 | Clemson University | 29200 | 37100 | 0.2141 | 23,401 | 1343 | 0.3834 | |
| 126 | University of Toledo | 29500 | 32600 | 0.0966 | 11,013 | 1229 | 0.9202 | |
| 127 | Michigan Technological University | 29700 | 34700 | 0.1442 | 6,013 | 1256 | 0.9243 | |
| 128 | Rochester Institute of Technology | 30500 | 78100 | 0.6093 | 14,267 | 1381 | 0.6693 | |
| 129 | Florida Agricultural and Mechanical University | 30600 | 38500 | 0.2052 | 7,890 | 1110 | 0.2056 | |
| 130 | California State University-Long Beach | 31000 | 38900 | 0.2032 | 36,082 | 1135 | 0.4627 | |
| 130 | West Virginia University Institute of Technology | 31000 | 39900 | 0.2231 | 1,278 | 1025 | 0.3668 | |
| 132 | University of California-Santa Barbara | 31100 | 59100 | 0.4735 | 23,181 | 1354 | 0.3297 | |
| 132 | University of North Dakota | 31100 | 33700 | 0.0785 | 11,033 | 1150 | 0.769 | |
| 134 | Rider University | 31300 | 60600 | 0.4832 | 3,145 | 1233 | 0.7864 | |
| 135 | Hampton University | 31400 | 54800 | 0.427 | 3,728 | 947 | 0.6225 | |
| 135 | Maine Maritime Academy | 31400 | 33400 | 0.06 | 945 | 1180 | 0.5414 | |
| 137 | The University of Tennessee-Knoxville | 32500 | 35100 | 0.0742 | 30,564 | 1302 | 0.416 | |
| 138 | Hendrix College | 32800 | 59300 | 0.4466 | 1,100 | 1260 | 0.5565 | |
| 138 | North Carolina State University | 32800 | 54800 | 0.4007 | 28,422 | 1378 | 0.4174 | |
| 140 | Prairie View A & M University | 32900 | 39600 | 0.1691 | 8,877 | 975 | 0.7931 | |
| 141 | University of Rhode Island | 33000 | 46400 | 0.2886 | 14,376 | 1148 | 0.7216 | |
| 142 | California Baptist University | 33500 | 65600 | 0.4893 | 8,417 | 1070 | 0.8488 | |
| 142 | Cleveland State University | 33500 | 37300 | 0.1019 | 9,482 | 1069 | 0.913 | |
| 144 | Auburn University | 33700 | 34100 | 0.0117 | 27,907 | 1324 | 0.4592 | |
| 145 | Oklahoma State University-Main Campus | 34000 | 41000 | 0.1701 | 22,364 | 1159 | 0.7504 | |
| 145 | University of Cincinnati-Main Campus | 34000 | 36100 | 0.0581 | 33,033 | 1264 | 0.8529 | |
| 147 | Illinois Institute of Technology | 34100 | 75200 | 0.5467 | 3,135 | 1307 | 0.5493 | |
| 148 | Milwaukee School of Engineering | 34300 | 70200 | 0.5117 | 2,704 | 1277 | 0.5893 | |
| 148 | University of Minnesota Duluth | 34300 | 39000 | 0.1194 | 8,426 | 1235 | 0.8875 | |
| 150 | The University of Tennessee-Chattanooga | 34500 | 34500 | 0 | 10,202 | 1140 | 0.8109 | |
| 151 | Missouri University of Science and Technology | 36200 | 56300 | 0.3578 | 5,552 | 1305 | 0.7255 | |
| 152 | Texas A&M University-Kingsville | 36500 | 41600 | 0.1237 | 5,386 | 1050 | 0.9092 | |
| 153 | Arizona State University Campus Immersion | 36600 | 47500 | 0.2296 | 65,450 | 1203 | 0.8989 | |
| 153 | SUNY College of Environmental Science and Forestry | 36600 | 40000 | 0.085 | 2,381 | 1239 | 0.6328 | |
| 155 | University of New Haven | 36900 | 67300 | 0.4515 | 4,903 | 1164 | 0.6038 | |
| 156 | University of Connecticut | 37300 | 53600 | 0.3043 | 20,056 | 1329 | 0.5239 | |
| 157 | Kettering University | 37500 | 71800 | 0.4776 | 1,212 | 1260 | 0.7867 | |
| 158 | Benedictine College | 37600 | 50800 | 0.2599 | 2,403 | 1241 | 0.9812 | |
| 158 | Virginia Polytechnic Institute and State University | 37600 | 66300 | 0.433 | 31,035 | 1366 | 0.5478 | |
| 160 | Drexel University | 39100 | 83200 | 0.53 | 13,309 | 1339 | 0.7944 | |
| 161 | New Mexico Institute of Mining and Technology | 39200 | 44400 | 0.116 | 1,066 | 1197 | 0.4449 | |
| 162 | University of Louisiana at Lafayette | 40300 | 44100 | 0.0862 | 13,432 | 1225 | 0.8701 | |
| 163 | Louisiana State University and Agricultural & Mechanical College | 40400 | 50000 | 0.1922 | 34,242 | 1273 | 0.7333 | |
| 164 | The University of Texas at San Antonio | 40800 | 48500 | 0.1587 | 31,127 | 1115 | 0.8679 | |
| 165 | Ohio State University-Main Campus | 41000 | 53600 | 0.2352 | 46,815 | 1378 | 0.6057 | |
| 166 | Colorado School of Mines | 41400 | 60100 | 0.3111 | 6,195 | 1399 | 0.6069 | |
| 167 | Rose-Hulman Institute of Technology | 41500 | 83200 | 0.5012 | 2,315 | 1404 | 0.7686 | |
| 168 | University of New Hampshire-Main Campus | 42600 | 56200 | 0.2421 | 11,355 | 1222 | 0.8816 | |
| 169 | University of Maryland-College Park | 43100 | 53600 | 0.196 | 31,133 | 1463 | 0.4479 | |
| 170 | Florida Institute of Technology | 43600 | 68700 | 0.3659 | 3,666 | 1224 | 0.577 | |
| 170 | Manhattan University | 43600 | 74100 | 0.4115 | 2,744 | 1274 | 0.7894 | |
| 172 | University at Buffalo | 43900 | 46700 | 0.06 | 20,359 | 1303 | 0.7418 | |
| 172 | University of Oklahoma-Norman Campus | 43900 | 57100 | 0.2305 | 23,329 | 1239 | 0.766 | |
| 174 | Oregon State University | 44900 | 61900 | 0.2746 | 31,253 | 1272 | 0.773 | |
| 175 | Widener University | 46000 | 78400 | 0.4132 | 2,975 | 1184 | 0.7093 | |
| 176 | University of California-San Diego | 46100 | 76000 | 0.3933 | 34,955 | 1375 | 0.2671 | |
| 177 | Michigan State University | 46200 | 56200 | 0.1779 | 41,234 | 1279 | 0.848 | |
| 177 | Rensselaer Polytechnic Institute | 46200 | 86300 | 0.4644 | 5,741 | 1438 | 0.6347 | |
| 179 | Rutgers University-New Brunswick | 47100 | 59700 | 0.2117 | 37,985 | 1390 | 0.5815 | |
| 180 | University of Colorado Boulder | 47300 | 57700 | 0.1805 | 32,244 | 1351 | 0.7808 | |
| 181 | Purdue University-Main Campus | 48600 | 51200 | 0.0517 | 44,819 | 1327 | 0.4987 | |
| 181 | Tulane University of Louisiana | 48600 | 91400 | 0.4684 | 8,192 | 1451 | 0.1398 | |
| 183 | University of Georgia | 48800 | 51600 | 0.0542 | 32,399 | 1382 | 0.377 | |
| 184 | Stevens Institute of Technology | 49700 | 85800 | 0.4206 | 4,236 | 1445 | 0.4758 | |
| 185 | The University of Texas at Austin | 49800 | 59400 | 0.1617 | 43,165 | 1356 | 0.2664 | |
| 186 | Worcester Polytechnic Institute | 50400 | 83600 | 0.397 | 5,558 | 1292 | 0.6016 | |
| 187 | University of Michigan-Ann Arbor | 50900 | 84700 | 0.3991 | 34,454 | 1435 | 0.1564 | |
| 188 | University of Minnesota Twin Cities | 53300 | 61000 | 0.127 | 41,303 | 1338 | 0.7975 | |
| 189 | The University of Alabama | 55800 | 56200 | 0.0071 | 34,389 | 1284 | 0.7665 | |
| 190 | Howard University | 60000 | 66500 | 0.0978 | 11,519 | 1208 | 0.4134 | |
| 191 | Hawaii Pacific University | 63700 | 65800 | 0.0327 | 3,533 | 1120 | 0.8587 | |
| 192 | University of California-Davis | 69800 | 69800 | 0 | 32,273 | 1290 | 0.4183 | |
| 193 | University of California-Berkeley | 70900 | 76100 | 0.0684 | 33,070 | 1407 | 0.1098 |
School data is from 2023–2024 (top 500 results shown) for schools with at least 100 undergraduate students.